The ratios of copper to zinc in alloys A and B are 3 : 4 and 5 : 9, respectively. A and B are taken in the ratio 2 : 3 and melted to form a new alloy C. What is the ratio of copper to zine in C?

Quantity of copper in alloy A = $$\frac{3}{3 + 4} = \frac{3}{7}$$ 
Quantity of zinc in alloy A = $$\frac{4}{3 + 4} = \frac{4}{7}$$
Quantity of copper in alloy B = $$\frac{5}{5 + 9} = \frac{5}{14}$$
Quantity of zinc in alloy B = $$\frac{9}{5 + 9} = \frac{9}{14}$$
A and B are taken in the ratio 2 : 3 and melted to form a new alloy C.
So,
Quantity of copper in alloy C = 2(quantity of copper in alloy A) + 3(quantity of copper in alloy B)
= $$\frac{2 \times 3}{7} + \frac{3 \times 5}{14} = \frac{6}{7} + \frac{15}{14} = \frac{27}{14}$$
Quantity of zinc in alloy C = 2(quantity of zinc in alloy A) + 3(quantity of zinc in alloy B)
= $$\frac{2 \times 4}{7} + \frac{3 \times 9}{14} = \frac{8}{7} + \frac{28}{14} = \frac{43}{14}$$
Ratio of copper to zine in C = $$\frac{27}{14} : \frac{43}{14}$$ = 27 : 43